On Unconstrained Quasi-Submodular Function Optimization

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which satisfies weaker properties than submodularity but still enjoys favorable performance in optimization. Similar to the diminishing return property of submodularity, we first define a corresponding property called the {\em single sub-crossing}, then we propose two algorithms for unconstrained quasi-submodular function minimization and maximization, respectively. The proposed algorithms return the reduced lattices in $\mathcal{O}(n)$ iterations, and guarantee the objective function values are strictly monotonically increased or decreased after each iteration. Moreover, any local and global optima are definitely contained in the reduced lattices. Experimental results verify the effectiveness and efficiency of the proposed algorithms on lattice reduction.Comment: 11 page

Light Propagation and Gas Absorption Studies in Turbid Media Using Tunable Diode Llaser Techniques

Optical absorption spectroscopy is a widely used analytical tool for constituent analysis in many applications. According to the Beer-Lambert law, the transmitted light intensity through a homogeneous medium is an exponential function of the product of the concentration, the total pathlength, and the absorption cross-section of the absorbing substance. By studying the intensity loss at the unique absorption band of the absorbing substance, its concentration can be retrieved. However, this method will encounter some difficulties if the light is not only absorbed but also strongly scattered in the material, e.g., in a turbid medium (biological tissues, porous ceramics, wood), which results in an unknown absorption pathlength. Such a problem can be solved by studying light propagation with different theoretical models, and the scattering and absorption properties are then retrieved. One aim of the present thesis work is to develop a new experimental approach to study light propagation in turbid media – frequency-modulated light scattering interferometry (FMLSI), originating from the well-known frequency-modulated continuous-wave technique in telecommunication field. This method provides new possibilities to study optical properties and Brownian motion simultaneously, which is particularly useful in biomedical applications, food science, and for colloidal suspensions in general. Another important application of absorption spectroscopy is to monitor gas concentration in turbid media, where the gas absorption pathlength is a priori unknown due to heavy light scattering in the porous medium. The technique is referred to as gas in scattering media absorption spectroscopy (GASMAS), and is based on the principle that the absorption spectrum of gases is much narrower than that for the solid- or liquid-phase host materials. By linearly scanning the wavelength of the light source across an absorption line of the gas and examining the absorption imprint superimposed on the transmitted light signal, the very weak intensity loss due to the gas of interest can be measured for gas concentration assessment. In order to obtain the absolute gas concentration, a focus in the present thesis work is to determine the gas absorption pathlength in turbid media. The FMLSI technique is proposed to obtain the mean optical pathlength – the total pathlength through both the pores and the matrix material. The combined method of FMLSI and GASMAS techniques is then developed to study porous media, where an average gas concentration in the porous media can be obtained. A conventional method for pathlength or optical properties determination – frequency domain photon migration – is also combined with the GASMAS technique to study the total gas absorption pathlength and the porosities of ceramics, which, as a result, also contributes to further understanding of light propagation in porous media. Another method is also proposed to get the absolute gas concentration without knowing the optical pathlength. It is based on absorption line shape analysis – relying on the fact that the line shape depends upon the concentration of the buffer gas. This method is found to be very useful for, e.g., gas concentration monitoring in food packaging